Fast and robust Block-Sparse Bayesian learning for EEG source imaging

Abstract

We propose a new Sparse Bayesian Learning (SBL) algorithm that can deliver fast, block-sparse, and robust solutions to the EEG source imaging (ESI) problem in the presence of noisy measurements. Current implementations of the SBL framework are computationally expensive and typically handle fluctuations in the measurement noise using different heuristics that are unsuitable for real-time imaging applications. We address these shortcomings by decoupling the estimation of the sensor noise covariance and the sparsity profile of the sources, thereby yielding an efficient two-stage algorithm. In the first stage, we optimize a simplified non-sparse generative model to get an estimate of the sensor noise covariance and a good initialization of the group-sparsity profile of the sources. Sources obtained at this stage are equivalent to those estimated with the popular inverse method LORETA. In the second stage, we apply a fast SBL algorithm with the noise covariance fixed to the value obtained in the first stage to efficiently shrink to zero groups of sources that are irrelevant for explaining the EEG measurements. In addition, we derive an initialization to the first stage of the algorithm that is optimal in the least squares sense, which prevents delays due to suboptimal initial conditions. We validate our method on both simulated and real EEG data. Simulations show that the method is robust to measurement noise and performs well in real-time, with faster performance than two state of the art SBL solvers. On real error-related negativity EEG data, we obtain source images in agreement with the experimental literature. The method shows promise for real-time neuroimaging and brain-machine interface applications.

Keywords: Block-sparse bayesian learning; Brain machine/computer interface; EEG source imaging; Empirical bayes; Error-related negativity; Evidence framework; Marginal likelihood; Real time.